deletions | additions       diff --git a/beginproblem_a_You_a.tex b/beginproblem_a_You_a.tex  index 5b58bec..3a3b08a 100644  --- a/beginproblem_a_You_a.tex  +++ b/beginproblem_a_You_a.tex 
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\end{problem}  \\ \\\\  \textbf{Solution 1: }  (a) Since we are receiving one extra coupon for each consecutive day: $1 + 2 + \ldots + (k-1) + k$, the total coupons received for $k$ days can be represented as $\sum\limits_{i=1}^k i$ = $\frac{k(k+1)}{2}$ 
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Hint: By hand, find the smallest $c$ for which $n=c$ satisfies this inequality, and  then prove by induction that it holds for all $n \ge c$.  \end{problem}  \\  \textbf{Solution 2: }  \\*  Base Case: For $n=3$ $2^3+3^3+4^3\leq5^3$